Stable Adaptive Reference Trajectory Modification for Saturated Control Applications Puneet Singla Kamesh Subbarao Assistant Professor Assistant Professor University at Buffalo University of Texas at Arlington Buffalo, NY 14260 Arlington, TX 76019 psingla@buffalo.edu subbarao@uta.edu Abstract— This paper will address the issue of reference trajectory modification in the presence of actuator satura- tion constraints. A stable adaptive trajectory modification scheme is proposed that ensures the stability of the closed loop system under actuator constraints. Also, the specific issues of the effects of actuator constraints on controller performance and stability is studied in detail. In partic- ular, the performance of the control law is evaluated by considering the spacecraft rendezvous problem with real- istic actuator constraints. The essential ideas and results from computer simulations are presented to illustrate the algorithm developed in paper. I. I NTRODUCTION Control saturation is one of the major challenges in in design of feedback control systems, wherein physi- cal limitations on actuators and/or the plant generally dictate the control input constraints either to avoid damage to or deterioration of the process. Thus, it is imperative that the control input does not exceed its bounds while simultaneously realizing the performance objectives. However, there may be some instances where input saturation may even be desired from an optimality point-of-view as in the case of bang-bang control for time optimal purposes [1]. As such, the actuator saturation issues and their effects on closed loop stability as well as performance is well- recognized and has received much attention from the control community. [2] presents an extensive summary of recent research results in designing and analyzing control schemes for systems with unknown actuator fail- ures and unknown parameters. The main focus in [2] is an adaptive actuator failure compensation approach that does not need an explicit fault detection and diagnosis procedure for failure compensation. Adaptive laws are designed that automatically adjust controller parameters based on system response errors. This allows an easy reconfiguration of the remaining functional actuators to accommodate a wide range of actuator failures and sys- tems parameter uncertainties (see [2] for more details). We further note that typical control law formulations normally do not incorporate any information about ac- tuator position or rate constraints [3]–[5] a priori. Of late however, a lot of work has been done to incorporate actuator constraints in control formulations, however, the stability of the resultant controller is still an issue [6]– [9]. In [10], the effect of input saturation was analyzed on feedback linearization and in design of controllers for stabilization and tracking. Also, for the feedback linearization controllers, the regions of attraction of the controllers were characterized ( [10])in addition to the space of feasible trajectories. The application of these controllers included aircraft flight control. Typi- cal scenarios of trajectory tracking wherein demanding reference trajectories resulted in actuator saturation were studied. In [11], a technique for avoiding input saturation was proposed by re-parameterizing the reference trajec- tory on a slower time scale. In that sense, this paper tries to achieve a similar objective albeit differently. The objective of this paper is to consider the effect of actuator position and rate constraints on the stability and performance of a model reference adaptive control system. The results of this paper can then be used as a basis for adaptive control formulation for a general non- linear system under actuation constraints. In particular, the performance of the control law will be evaluated by considering the relative spacecraft position and attitude control problems with realistic actuator constraints. The rest of the paper is organized as follows. We first introduce the class of nonlinear dynamical systems under study. Nominal control laws to meet a desired tracking trajectory are outlined. This is followed by a detailed discussion on an adaptive reference trajectory modification algorithm when control saturation occurs. Simulation results are presented for a spacecraft ren- dezvous problem followed by the summary and conclu- sions. 2008 American Control Conference Westin Seattle Hotel, Seattle, Washington, USA June 11-13, 2008 ThC16.3 978-1-4244-2079-7/08/$25.00 ©2008 AACC. 3470